lie-algebras-and-their-representations

Source code for my notes on representations of semisimple Lie algebras and Olivier Mathieu's classification of simple weight modules

git clone: git://git.pablopie.xyz/lie-algebras-and-their-representations
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Commit: 65e93388cd80c096674dbfa5510dedb2ce0c8165
Parent: c37732113c53393e5b48794104a7547dccf0cfc0
Author: Pablo <pablo-escobar@riseup.net>
Date: Fri, 21 Apr 2023 15:20:17 +0000

Added some qualifiers to the statement about the Lie functor for algebraic groups

Diffstat

1 file changed, 4 insertions, 3 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/introduction.tex	7	4	3

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -274,9 +274,10 @@ there is no rational group homomorphism \(\mathbb{C} \to
 In particular, the Lie functor
 \(\mathbb{C}\text{-}\mathbf{Grp}_{\operatorname{simpl}} \to
 \mathbb{C}\text{-}\mathbf{LieAlg}\) -- between the category
-\(\mathbb{C}\text{-}\mathbf{Grp}_{\operatorname{simpl}}\) of complex algebraic
-groups and the category of complex Lie algebras -- fails to be full. Similarly,
-the functor \(\mathbb{C}\text{-}\mathbf{Grp}_{\operatorname{simpl}} \to
+\(\mathbb{C}\text{-}\mathbf{Grp}_{\operatorname{simpl}}\) of simply connected
+complex algebraic groups and the category of complex Lie algebras -- fails to
+be full. Similarly, the functor
+\(\mathbb{C}\text{-}\mathbf{Grp}_{\operatorname{simpl}} \to
 \mathbb{C}\text{-}\mathbf{LieAlg}\) is \emph{not} essentially surjective onto
 the subcategory of finite-dimensional algebras: every finite-dimensional
 complex Lie algebra is isomorphic to the Lie algebra of a unique simply